If the distance between the earth and the sun becomes `1//4th` of its present value, then its period of revolution around the sun will become

Options

A. `((365)/(4))`days
B. `(365xx4)` days
C. `(365xx8)` days
D. `((365)/(8))` days

Answer

D

Explanation

`because T^(2)prop R^(3)`
`therefore (T_(2)^(2))/(T_(1)^(2))=(R_(2)^(3))/(R_(1)^(3))=(((R_(1))/(4))/(R_(1)))^(3)=(1)/(64)`
`therefore ((T_(2))/(T_(1)))^(2)=((1)/(8))^(2)`
`therefore (T_(2))/(T_(1))=(1)/(8)` or `T_(2)=(T_(1))/(8)=((365)/(8))` days